Generalized Higher-Order Derivative Optimality Condition For Super Efficient Solutions Of Set-valued Optimization

In normal linear spaces super efficient solutions of set-valued optimization are investigated with generalized higher-order cone-directed adjacent derivatives. Under the assumption of near cone-subconvexlikeness, with the help of separate theorem for convex sets and the properties of Henig expansion cone, the type of Fritz John necessary optimality condition is established for set-valued optimization problem to obtain its super efficient elements.Under the assumption of near cone-subconvexlikeness and generalized cone-convex, with the help of separate theorem for convex sets and the scalarization on super efficiency, in normal linear spaces a higher order Mond-Weir type dual problem of set-valued optimization are investigated with generalized higher-order cone-directed adjacent derivatives.